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E8 Structure Decoded
arobic writes "A group of mathematicians from US and Europe succeeded in mapping the E8 structure, an example of a Lie group. These were developed by the well-known mathematician Sophus Lie (pronounce Lee) in the last century and are used for many applications, mainly in theoretical physics. This is an important breakthrough as it could help physicists working on Grand Unified Theories (aka GUTs)."
Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.
The magnitude and nature of the E8 calculation invite comparison with the Human Genome Project. The human genome, which contains all the genetic information of a cell, is less than a gigabyte in size. The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes. This is enough to store 45 days of continuous music in MP3-format.
Hear that? That's the sound of Apple's iPod marketing finally reaching absolute ubiquity.
-The Wolf
Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.
It's PRINCESS "Lee-eh" you insensitive clod!
Help! I've fallen in a karma hole and I can't get up!
http://en.wikipedia.org/wiki/E8_(mathematics)
Seriously, these articles, as most in Math category, are totally undecipherable to most normal users. TG there is a Wikipedia somewhere, sometimes they are closer to layman.
But of course it has practical applications: it applies to string theory!
E8 is not a Lie Group. E8 is the biggest Lie Group. Here are a few links for more accurate info:
. stm
http://news.bbc.co.uk/2/hi/science/nature/6466129
http://en.wikipedia.org/wiki/E8_(mathematics)
Write your own Choose Your Own Adventure. http://www.freegameengines.org/gamebook-engine/
Apologies -- this post uses a lot of technical jargon. However, the article is so badly written that I decided to post some remarks. And yes, I am a professional mathematician.
First, what they mapped was not the "structure" of the Lie group E_8 -- the structure of the group has been known for a long time. What they mapped is what are called the "representations" of the group E_8, which is part of Vogan's program to understand the "unitary dual" (=list of representations) for all (reductive) Lie groups.
Second, this has no relevance to grand unified theories. Even though a (compact) form of E_8 can be the gauge group of a GUT, the relevant representations are finite-dimensional and have been classified by Weyl decades ago.
Finally, this is an important result. It is relevant to number theory, and to abstract mathematics in general. The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.
"The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes. This is enough to store 45 days of continuous music in MP3-format."
Because we know physicsts and mathematicians that would be interested in this problem would have no idea how a computer works and have to translate it into teenager speak.
God spoke to me.
is, of course the third worst in the universe.
So now we're going to have truth and lie tables?
Stop this crazy planet. I want to get off!
Dedicated Cthulhu Cultist since 4523 BC.
Hello:
n tum/standard_model/standard_model.html
The standard model has the symmetries U(1)xSU(2)xSU(3). The one in the middle, SU(2), is a unit quaternion, where a quaternion is like a real or complex number, but has four parts. I have developed the software to visualize quaternions at http://quaternions.sf.net/ using one number for time, three for space. SU(2) can be represented by the quaternion function exp(q-q*). Feed a thousand random quaternions into exp(q-q*), and get POVRay to make a nice animation. Do the same for q/|q| exp(q-q*), and you have a visual representation of the electroweak symmetry. Smash two of these together, and you get the symmetry of the standard model.
Visually, there is a clear message: if you want to smoothly represent all possible events in spacetime as quaternions, the group description must be U(1)xSU(2)xSU(3). You won't read that in a journal because it has to be done with animations.
http://www.theworld.com/~sweetser/quaternions/qua
doug
Working on new views of old physics at http://VisualPhysics.org
the answer is 42!
Typical geek attitude. If it's not Vorbis, it's LAME.
Step into a huge movement. Don't Tread In Me.
This post climbed Mt. Washington.
Category theorist John Baez has a summary of this work from a mathematician's perspective. Unfortunately, you need at least an undergraduate math degree to make full sense of it, but it gives more flavor of what's really going on than a news story, and he at least defines mathematically what E8 and KLV polynomials are.
He begins by noting, "You may hear some hype about this soon, because it's a really big calculation, and the American Institute of Mathematics has coaxed a lot of science reporters to write about it -- in part by comparing it to the human genome project. Computing the Kazhdan-Lusztig-Vogan polynomials for E 8 is certainly nowhere nearly as important as the human genome project, nor as hard! But the final result involves more data, in a sense."
E8 is not a finite group so it cannot be embedded in a finite symmetric group.